Question

In: Economics

Imagine you consume two goods, X and Y, and your utility function is U = X1/2Y1/4....

Imagine you consume two goods, X and Y, and your utility function is U = X1/2Y1/4. Your budget is M = 630; PX = $10; PY = $30. Now imagine PX increases to $25. The compensated price bundle is (30.9458, 12.8941). What is the income effect on X?

Solutions

Expert Solution

U=X^(1/2) Y^(1/4)

MRS= -MUx/MUy= -(0.5/0.25)(y/x)= -2y/x

New Budget line Equation:

25X+30Y= 630

-Px/Py= -25/30= -5/6

At equilibrium

MRS=Px/Py

-2y/x=-5/6

12y=10x

1.2y=x

25*1.2y+30y=630

60y=630

y*= 10.5

x*= 1.2*10.5= 12.6

New demand for good x= 12.6

Compensated demand for good x= 30.9458

Income effect= compensated demand- New demand= 18.3458

Income effect on good x= 18.3458

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

Imagine you consume two goods, X and Y, and your utility function is U = X1/2Y1/4....
Imagine you consume two goods, X and Y, and your utility function is U = X1/2Y1/4. Your budget is M = 630; PX = $10; PY = $30. Now imagine PX increases to $25. The compensated price bundle is (30.9458, 12.8941). What is the income effect on X?
Imagine you consume two goods, X and Y, and your utility function is U = XY....
Imagine you consume two goods, X and Y, and your utility function is U = XY. Your budget is $100, the price of Good X is $4, and the price of Good Y is $25. So, the optimal bundle for you to consume is (12.5, 2). Now the price of good X increases to $10. The compensated price bundle is (7.91, 3.16). What is the income effect on X?
1. Imagine you consume two goods, K and L, and your utility function is U =...
1. Imagine you consume two goods, K and L, and your utility function is U = K1/3L2/3. Your budget is $120; PK = $6; PL = $9. So, the optimal bundle for you to consume is (K = 6.6667, L = 8.8889). Now, suppose the price of good K increases to $9. What is the new optimal K for you to consume? 2. Imagine you consume two goods, K and L, and your utility function is U = K1/3L2/3. Your...
A consumes two goods, x and y. A ’s utility function is given by u(x, y)...
A consumes two goods, x and y. A ’s utility function is given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of y is 1. A has an income of M. (a) Derive A ’s demand functions for x and y. (b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution effects of the price change. (c) Calculate the compensating variation of the price change....
Suppose both Smith and Jones utility functions of U(X,Y) = X1/2Y1/2. Smith is endowed with (X,...
Suppose both Smith and Jones utility functions of U(X,Y) = X1/2Y1/2. Smith is endowed with (X, Y) = (9,25) and Jones is endowed with (X, Y) = (25,9). a. Draw an Edgeworth box with indifference curves through this endowment. b. At what combinations of X and Y are both better off (i.e., are Pareto Improving)? c. At what combinations of X and Y are there no more gains from trade (i.e., are Pareto Efficient)? d. If they agreed on a...
An individual likes to consume 2 goods X and Y . The utility function for this...
An individual likes to consume 2 goods X and Y . The utility function for this individual is U = X+0.5Y . What is the marginal utility of X and Y ? The individual has an income of $90. The price of X is $10 and the price of Y is $5. What is the optimal consumption bundle of this individual? Graph the individuals optimal bundle with the budget line and indierence curve. (answer: Infinitely many solutions). Do the same...
Esther consumes goods X and Y, and her utility function is      U(X,Y)=XY+Y For this utility function,...
Esther consumes goods X and Y, and her utility function is      U(X,Y)=XY+Y For this utility function,      MUX=Y      MUY=X+1 a. What is Esther's MRSXY? Y/(X + 1) X/Y (X + 1)/Y X/(Y + 1) b. Suppose her daily income is $20, the price of X is $4 per unit, and the price of Y is $1 per unit. What is her best choice?      Instructions: Enter your answers as whole numbers.      X =      Y =      What is Esther's utility when her...
A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...
A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x) + 3y. For this utility function MUx =1/x and MUy = 3. The price of x is px = 4 and the price of y is py = 2. The consumer has M units of income to spend on the two goods and wishes to maximize utility, given the budget. Draw the budget line for this consumer when M=50 and the budget line when...
13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y)...
13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of y is 1. Pip has an income of M. (a) Derive Pip’s demand functions for x and y. [5 marks] (b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution effects of the price change. [5 marks] (c) Calculate the compensating variation of...
Leon consumes two goods, X and Y. His utility function is given by U(X,Y) = 56XY....
Leon consumes two goods, X and Y. His utility function is given by U(X,Y) = 56XY. The price of X is $14 a unit; the price of Y is $8 a unit; and Leon has $672 to spend on X and Y. a. Provide the equation for Leon’s budget line. (Your answer for the budget line should be in the form Y = a – bX, with specific numerical values given for a and b.) b. Provide the numerical value...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT